{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python for Finance (2nd ed.)\n",
    "\n",
    "**Mastering Data-Driven Finance**\n",
    "\n",
    "&copy; Dr. Yves J. Hilpisch | The Python Quants GmbH\n",
    "\n",
    "<img src=\"http://hilpisch.com/images/py4fi_2nd_shadow.png\" width=\"300px\" align=\"left\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mathematical Tools"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from pylab import plt, mpl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('seaborn')\n",
    "mpl.rcParams['font.family'] = 'serif'\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "uuid": "2326c3ad-f244-4f48-8b68-851bd2347d57"
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.sin(x) + 0.5 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_plot(x, y, styles, labels, axlabels):\n",
    "    plt.figure(figsize=(10, 6))\n",
    "    for i in range(len(x)):\n",
    "        plt.plot(x[i], y[i], styles[i], label=labels[i])\n",
    "        plt.xlabel(axlabels[0])\n",
    "        plt.ylabel(axlabels[1])\n",
    "    plt.legend(loc=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "uuid": "c09f73d2-c2a5-4c6d-a2f1-08a191378417"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-2 * np.pi, 2 * np.pi, 50)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false,
    "uuid": "96d2bd1b-8883-486d-920d-b610aeb076a8"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([x], [f(x)], ['b'], ['f(x)'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_01.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Monomials as Basis Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "res = np.polyfit(x, f(x), deg=1, full=True)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 4.28841952e-01, -1.31499950e-16]),\n",
       " array([21.03238686]),\n",
       " 2,\n",
       " array([1., 1.]),\n",
       " 1.1102230246251565e-14)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "uuid": "ace90420-7219-4227-8210-bf107f556726"
   },
   "outputs": [],
   "source": [
    "ry = np.polyval(res[0], x)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "uuid": "c0667d3e-a48a-413d-b250-5e0d3b58275e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([x, x], [f(x), ry], ['b', 'r.'],\n",
    "            ['f(x)', 'regression'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_02.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "uuid": "096bb07a-55f7-45de-8734-2a76d8749d53"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(x, f(x), deg=5)\n",
    "ry = np.polyval(reg, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "uuid": "5e17309e-e8e2-4df9-b841-0f57d983b89e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([x, x], [f(x), ry], ['b', 'r.'],\n",
    "            ['f(x)', 'regression'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_03.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "uuid": "67b14a21-e8f2-4dd4-a43b-0d232f2b4055"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(x, f(x), 7)\n",
    "ry = np.polyval(reg, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "uuid": "e600b6be-4cf2-4212-807a-7f397f081e98"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(f(x), ry)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "uuid": "bc6918fe-f520-483c-94eb-41dd89abfa70"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0017769134759517689"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean((f(x) - ry) ** 2)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "uuid": "053752b7-7eb3-4d93-acdf-69874ceada12"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([x, x], [f(x), ry], ['b', 'r.'],\n",
    "            ['f(x)', 'regression'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_04.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Individual Basis Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "uuid": "b4f05890-56e0-4f29-9d61-bd9948ad8af0"
   },
   "outputs": [],
   "source": [
    "matrix = np.zeros((3 + 1, len(x)))  \n",
    "matrix[3, :] = x ** 3  \n",
    "matrix[2, :] = x ** 2  \n",
    "matrix[1, :] = x  \n",
    "matrix[0, :] = 1  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "uuid": "c8963eee-4bc8-4ef2-a172-d4b64fd065a3"
   },
   "outputs": [],
   "source": [
    "reg = np.linalg.lstsq(matrix.T, f(x), rcond=None)[0]  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "uuid": "efd077d1-9c8a-4961-be95-400f83cd679e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.    ,  0.5628, -0.    , -0.0054])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.round(4)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "uuid": "efb7b252-d0f8-4263-b2be-4d9588ab06a7"
   },
   "outputs": [],
   "source": [
    "ry = np.dot(reg, matrix)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "uuid": "1b1953fe-83a2-436b-8cd4-69c5abf6d2e1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([x, x], [f(x), ry], ['b', 'r.'],\n",
    "            ['f(x)', 'regression'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_05.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "matrix[3, :] = np.sin(x)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "reg = np.linalg.lstsq(matrix.T, f(x), rcond=None)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "uuid": "86f9a92c-600d-4515-b34d-20c9f35a86b0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0. , 0.5, 0. , 1. ])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.round(4)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "uuid": "ac77ef01-8abe-4b99-8f92-8325a396ff2c"
   },
   "outputs": [],
   "source": [
    "ry = np.dot(reg, matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "uuid": "02481bd5-c737-46bc-9b90-5554fcad8745"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(f(x), ry)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "uuid": "6bf80137-3a52-483b-a557-b092bbf23b36"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.404735992885531e-31"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean((f(x) - ry) ** 2)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "uuid": "58d9db31-5885-4fba-8ae7-2e962a0963ca"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([x, x], [f(x), ry], ['b', 'r.'],\n",
    "            ['f(x)', 'regression'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_06.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Noisy Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "uuid": "75d3a6a6-a940-4a49-b35d-29f21880ab95"
   },
   "outputs": [],
   "source": [
    "xn = np.linspace(-2 * np.pi, 2 * np.pi, 50)  \n",
    "xn = xn + 0.15 * np.random.standard_normal(len(xn))  \n",
    "yn = f(xn) + 0.25 * np.random.standard_normal(len(xn))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "uuid": "f6f9c05f-1f96-48ee-aaca-f4d80c3d3ac5"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(xn, yn, 7)\n",
    "ry = np.polyval(reg, xn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "uuid": "9a475222-3bfd-4300-951b-94e60792c6da"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([x, x], [f(x), ry], ['b', 'r.'],\n",
    "            ['f(x)', 'regression'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_07.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Unsorted Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "uuid": "8ea85cdb-47f2-4967-b684-7894d9964e76"
   },
   "outputs": [],
   "source": [
    "xu = np.random.rand(50) * 4 * np.pi - 2 * np.pi  \n",
    "yu = f(xu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "uuid": "0034edf5-1cef-4eea-be44-c69103fe6eb2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 5.19  5.44  0.31  6.03 -5.98 -0.25 -0.35 -2.38  0.89 -0.7 ]\n",
      "[ 1.71  1.97  0.45  2.76 -2.69 -0.37 -0.51 -1.88  1.22 -0.99]\n"
     ]
    }
   ],
   "source": [
    "print(xu[:10].round(2))  \n",
    "print(yu[:10].round(2))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "uuid": "d7f5f003-1cb8-4432-a8d6-cb4bef1a101a"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(xu, yu, 5)\n",
    "ry = np.polyval(reg, xu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "uuid": "40177962-0363-479c-bdbd-451a4c043060"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([xu, xu], [yu, ry], ['b.', 'ro'],\n",
    "            ['f(x)', 'regression'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_08.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Multiple Dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "uuid": "82b95a7b-9e3e-4dc8-b313-1af775b06b8b"
   },
   "outputs": [],
   "source": [
    "def fm(p):\n",
    "    x, y = p\n",
    "    return np.sin(x) + 0.25 * x + np.sqrt(y) + 0.05 * y ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(0, 10, 20)\n",
    "y = np.linspace(0, 10, 20)\n",
    "X, Y = np.meshgrid(x, y)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "uuid": "b03b67ac-f7df-41d1-9dab-1e074e8738fa"
   },
   "outputs": [],
   "source": [
    "Z = fm((X, Y))\n",
    "x = X.flatten()  \n",
    "y = Y.flatten()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "uuid": "52a91ef7-33c4-4de1-b69b-ea4d740aa252"
   },
   "outputs": [],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "uuid": "52a91ef7-33c4-4de1-b69b-ea4d740aa252"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x119129c50>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.gca(projection='3d')\n",
    "surf = ax.plot_surface(X, Y, Z, rstride=2, cstride=2,\n",
    "                       cmap='coolwarm', linewidth=0.5,\n",
    "                       antialiased=True)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('f(x, y)')\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "# plt.savefig('../../images/ch11/math_09.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "uuid": "5918f2cf-3ead-4b80-980e-4a375ee159db"
   },
   "outputs": [],
   "source": [
    "matrix = np.zeros((len(x), 6 + 1))\n",
    "matrix[:, 6] = np.sqrt(y)  \n",
    "matrix[:, 5] = np.sin(x)  \n",
    "matrix[:, 4] = y ** 2\n",
    "matrix[:, 3] = x ** 2\n",
    "matrix[:, 2] = y\n",
    "matrix[:, 1] = x\n",
    "matrix[:, 0] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "uuid": "b9eb74bd-9280-4d8b-ae7d-8853911389cb"
   },
   "outputs": [],
   "source": [
    "reg = np.linalg.lstsq(matrix, fm((x, y)), rcond=None)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "RZ = np.dot(matrix, reg).reshape((20, 20))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "scrolled": true,
    "uuid": "096451ce-173a-43b5-b81f-9dac26df2702"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x1197a1b70>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.gca(projection='3d')\n",
    "surf1 = ax.plot_surface(X, Y, Z, rstride=2, cstride=2,\n",
    "            cmap=mpl.cm.coolwarm, linewidth=0.5,\n",
    "            antialiased=True)  \n",
    "surf2 = ax.plot_wireframe(X, Y, RZ, rstride=2, cstride=2,\n",
    "                          label='regression')  \n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('f(x, y)')\n",
    "ax.legend()\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "# plt.savefig('../../images/ch11/math_10.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "uuid": "5e345542-f425-4630-9eae-0a446927ad73"
   },
   "outputs": [],
   "source": [
    "import scipy.interpolate as spi  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "uuid": "20200433-3e90-4bb6-be5a-8e6a1360989e"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-2 * np.pi, 2 * np.pi, 25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "uuid": "6e3caa90-2a2a-4429-8536-ab25091a5640"
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.sin(x) + 0.5 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "uuid": "afdb9c45-1b12-4358-ba3e-a1bc3c4d32db"
   },
   "outputs": [],
   "source": [
    "ipo = spi.splrep(x, f(x), k=1)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "uuid": "7217594a-3398-4dfd-9d16-f90ee0f24bd9"
   },
   "outputs": [],
   "source": [
    "iy = spi.splev(x, ipo)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "uuid": "b9cacc73-786b-4c6b-ad5f-e4d22729c17e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(f(x), iy)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "uuid": "89d96d0e-dabd-490f-acad-15bba904b546"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([x, x], [f(x), iy], ['b', 'ro'],\n",
    "            ['f(x)', 'interpolation'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_11.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "uuid": "3daf1f42-54d8-4150-aab6-5188d1c23bdb"
   },
   "outputs": [],
   "source": [
    "xd = np.linspace(1.0, 3.0, 50)  \n",
    "iyd = spi.splev(xd, ipo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "uuid": "7ba1134b-ac71-4c3a-a0fc-b644c59effc6"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7Gjdut2v8oIMOon79+hQW/kV6emM2bPh51ypZpCgJE5GICATgk09sPPqok//+N/hfzckn+xg82M2//+2Lep+pulBsHyk1qR+rzdoxCF6uvOACLxdc4OXHH4OXoWfPdjBmjIvcXCcXX+zh+us9ZGXpUmUkRWJ1d+cG3o8//ijbt2/jxx+/p337Trz77nx++OE71qxZzTHHtMbpdPL44xM58sij6d27L1OmPMbMmc9RXFzMoYcehs1m45133mT79u3MmTOLXr2u2vUaTqeLF1+cyW+/beCwww7n1FM7Y7FYWLVqBVOnPkEgEKBt2+M45ZSOvPfeArZv386bb+aRnX0Wr7zyMo8+Oo6MjKaUlZUyd+5bXHDBhXTo0IlZs2ZSXl6O3X4FP/zwHe++O582bY5l5MgxTJ36BIcd1oKff17PgAGD+OuvP/nkk4/Ztm0bGzb8wrvvzmfTpt9ZtuxzTj65/QF9X7SBdxjqm5Kcc4fknn9tzD0QgPfeszFpkovly4MNpP75Ty+DB5dz6qnRT752qs6ejIn6va9OT7GMjAYUPTOjVnuPhVNUBLNnO3juOeeujcY7d/Zy/fXBO2Gj3XcsUb/v1RWv8//yy2UsWDCXe+4ZGbHXSLo+YSKSmAKB4J2OZ56ZRu/eaSxfbuO88zwsXFhMXl4pp50WuQSsOv2PSgYNDfnYeCq2jxR3Tk+Knp6ON6stAbsdb1bbkIlVNHqPATRsCP37e/jf/4p58cUSTj/dy5Ildvr0SaVjx3o8+6yDMCVFkiRKSop3rah9883XsQ4nYrQSFka8fjKIhmSeOyT3/Pd37l98YeX++1NYtsyG1RogJ8fLbbeV06ZN5C8x1WZ3+2T/3gfsdiwhGm8G7Hb++C2yzSwLCqw895yD115zUFZmoUkTPwMGlNOnjyfie4Am8/cdknv+WgkTkTpr/XoL11+fQteu9Vi2zEbXrh6WLi3mqafKopKAQey72yeScD3GwtWO1Wb39TZt/OTmuvnqq2IGD3bjdlsYNSqFk0+ux6RJTrYlZ44gCU5JmIjU2N9/w8iRLk47rR5vveXgxBN9vP12CTNmlHH00dFdXU/mgvvaVt1LtjtXH+0Fq7D4fLvafdTGNjgHHxxg+PByli/fzrBhbnw+C2PHuvjHP+ozbpyTrVsP+CVE4oaSMBGpNo8HnnvOQYcO9ZgyxUmzZgGmTi1lwYISOnYMv39cJNVk9UYqF0+1YwcdBMOGlfPll9u55x43NluACROCydjYsU7+/DNGd3iI1CIlYSJSpUAA5s+3c/rp9bj77hQ8Hgv33efmk0+K6dHDizVC/5Oo4D76qnPJNpqrjw0awMCB5SxbVsz995eRmhpg0iQXJ51Uj1GjXPwVm32XRWqFkjARqZRpWsnJSaVv31TWr7fQr185n31WzK23lpOSErnXre4lr+qu3kjtqenqY23Uj9WvDwMGeFi2rJgxY8po2DDAk086ad++Po895qS0tMZPKRJzSsJEJCS3G8aPd3LWWWksXWrnnHO8fPxxCQ8/7KZJk8jXfangPn7VZPWxtuvHUlPh+us9fP55MQ8+WIbNBqNHu+jYsR4vv2wnxM2dInFLSZiIVPD551b+9a80xo930aRJgBdeKOHFF0tp1Sp6Xc1VcB+/arL6GKn6sZSUYK+xzz/fzsCBbgoLLQwalMqZZ6bx3ns26mD3JUlCSsJEZJeiIrjzThfduqXx3XdW+vUrZ8mSYs49N/rLCyq4j2/VXX2MdDLdqBHcc0/wEvmVV5azdq2Vq65K46KLUlm+XG9xEt/0EyoiACxYYCcrC2bMcNK6tZ933gleemzQoHZfp7r1QSq4TwzR6j3WvHmARx91s2hRCV26ePn0UzvnnVePa69N4ccfdSelxCclYSJJbtMmC9dem0KfPqls2QJ33OHmgw9KaN++9i891qQ+SAX3iSHavccyM/3MmlXKW2+VcNJJPt55x0HnzvW47z4XRUX7PQ2RiFASJpKkAgGYNcvBaafV4513HLRv7+Xrr+H228txuSLzmjWtD1LBfd0Xq95jnTr5mD+/hGnTSmnRIsDTTzvp2LEec+bY8UevtFGkUkrCRJLQpk0WevVKZciQFPx+GDeujLffLqVNm8i+rortk1Oseo9ZLNCtm5ePPy7m7rvdFBdbuO22VC64II1vv9Xbn8SefgpFkswHH9g488w0/vMfO2ed5eWTT4rp29cTsYare1KxvYQTydqxlBQYNKicTz4ppnt3D8uW2Tj77DSGDXNRWFgr4YvsFyVhIkmirAzuucfFFVekUVRkYcyYMmbPLqV589q5l1/d7eVARKN2rEWLAM89V0ZeXgmtWvl5/nknnTrV45lnUH8xiQklYSJJYM0aK+eck8azzzpp3drHwoUlXH+9B0st3TSm7vZyoKJZO/bPf/r46KMSRo4sw+220L8/nHtuGsuW6S1RossSqIMd7bZs2RbxoDMyGrBly7ZIv0xcSua5Q2LNPxCAmTMd3H+/i7IyC336lDNqlJu0tNDn7+/c07M7YS9YVWHcm9WWwkVLa/x8sZJI3/uaqitzb9I8HUuIZauA3c4fv9V8I8lNmyw88kh9Zs0Kfn3FFeXcf7+b9PQDjbTuqCvf+0iI1twzMhqE/MirtF8kQf35p4U+fVK4884UUlNh5sxSxo8Pn4AdCBXcS7TUdl1hs2YBXnwR3n67hKwsHy+/7KRz53q8/bZdXfcl4pSEiSSgjz+2ccYZaSxc6KBzZy+LFhVz/vneiL2eCu4lWmpaV1jdIv6OHX28/34J997rZts2C9ddl0qfPils3KhGrxI5SsJEEojPB2PGOLnkklT+/NPCvfe6ee21Ayu+V8G9xJOa1BXWtIjf4YDbbitn0aJiTj3Vu+NDTD2ef96h3mISEUrCRBJEYSH06pXK5MkujjgiwLx5Jdx2Wzk22/4/pwruJR5Vt4nv/hbxH310gDfeKCU3twyLBYYNSyEnJ5Xvv9eqmNQuJWEiCWDVKitdutRj8WI7Z5/t5f33iznxxAP/6F6TNzF1t5d4cyC1ilYr9O7tYcmSYs4/38Onn9o588x6TJrkxOOp7UglWSkJE6nj3nrLTteuaaxfb2XIEDcvvlhKo0a189wquJe6rDYawB5ySICZM8uYNq2URo0CjB3rokuXNL7+Wm+fcuD0UyRSR/l88OCDTq6/PhWLBWbMKOWuu8prtfO9Cu6lLqt2reKcOVVedu/WzcuSJcVceWU5q1bZOPfcNMaOdVJeHskZSKJTEiZSBxUWwhVXpPL44y6OPtrPwoUldO1a/bsfq3vHmArupS6rdq3i2LEhH7/vZfeDDoJHH3Xz+usltGgRYNIkF+eem0ZBgd5KZf/oJ0ekjlm9Olj/9Z//2Pn3v728+24xhlH9+q+a3DGmgnup66pVq7h6dcjHhrvsfvrpPv7zn+Cq2MqVwX0on3zSoa2PpMaUhInUIW+/bef883fXf82aVfP6r5reMaaCe0l4WVkhhyurHTuqdTozv/wHH9/8PA0bBhg1KoUePVJZv153UEr1KQkTqQP8/mD/r+uuSwVg+vT9r/9Ssb3IPu6+O+RwdTYPP31KX76+64Vdd1CecUY9Xn5Z3falepSEicS50lK47roUJk92cdRRwfqvCy7Y/+73KrYX2UevXge0eXiz6bnMmFHGE0+UYrXCoEGpXH11Kps3a1VMKqckTCSO/fUXXHJJKnPnOjj11GD9V2Zm+PovdbcX2T/Vuexe2SqyxQKXXupl8eJiTj/dy7vv2snOTmPePHukQ5c6TEmYSJz6+WcLF1yQxuef28nJ8fDKK6UcdFD489XdXiSyqrOK3KJFgNdeK2XMmDLOL3qFf1zTgcbN0ml0evi7kCV5KUUXiUPffmvliitS2bzZyoAB5dx3n7vK+q/KCu73TbDcOT2VdInUUMmgoTTs36/i+D6ryFYr3NJkNg09O84NgM1chbN/P4pA//ZkF62EicSZjz6y0b17Glu2WBg7toz77686AQMV3ItEWk1WkcN9KCq9/1EV7csuWgkTiSMvv2xn6NAUHA6YPr2sRg1Yfa0zsResCjkuIrWjuqvI4T78NP69gO59Upg0qYzGjWs7OqlrtBImEgcCARg/3smgQak0bAh5eTXrgA8quBeJJ+E+/Kyv14aFCx2ceWY9li61RTkqiTdKwkRizOOBwYNdjB/vomVLP/PmFdO+/d53QFbnrkcV3IvEj3AfippMGMzdd7vZvNlCjx6pjBvnxLv/HWekjtPlSJEY2r4drrsulY8+snP88T5eeqmUpk33LhjZedfjTjvvegxV4KuCe5H44M7pSRHBG2Nsa9fga51JycAheHJ6MohyTj3Vy403pjJhgouUN/O42/IQKT/uOG/QUP07ThIRTcIMwzgEGA0cb5rmKSGOpwNPA98ArYElpmk+G8mYROLF339Dr15pLF9u41//8vLss6XUr1/xvJrc9Sgi8aOyD0Xt2/v56KNi8i97izu+6r1rvLIPWZJ4In05sjPwFhCubfANwEbTNMcAg4DHDcPQJVJJeH/+aaFHj2ACdsklHl58MXQCBrrrUSRRHXQQDCl7OOSxcHu5SmKJaMJjmmYesK2SUzYBGTv+nAF8bZpm+HbgIglgZy3IihU2evcu5/HHy7BXsiatbYZEEpc+ZCU3SyDCDUsMwzgDmGCa5skhjtmBOcBmIAuYbprmC1U9p9frC9jtuqtE6p5ff4V//QtME2acM4c+v43Fsno1ZGUFNxHu1avig+bMgcsvrzg+e3bo80Wk7mjXDlasqDC8yt6OPz/8hn/+MwYxSSSEvCIY68L8ccBy0zQfMgwjFVhrGMZy0zQrNjvaQ2FhScQDy8howJYtlS3iJa5knjtEbv4//2zh4ovTWL/eyvQuL9L33at3H1yxAi6/nKKi0op1IP/qiuvp6RUKfN3/6gq1HKe+98k7f809NnN33TI4ZBf+Mb67ePWsAPfe6+bmmz1YIrgXuL73kZ97RkaDkONRr78yDKOeYRg7L0EeDmwEME2zFPgbcEU7JpFI+/FHCxdeGEzAhg1z0/uXR0KeF64OpDqbC4tI3ROutczlb11IkyYBRo1KoV+/FIqKYh2pREKk747MBnoDzQ3DuBfIBfoCxwE3AiOA0YZhtACaAq+bpvllJGMSiTbTtNKzZyqbNlm59143t91Wjm2i6kBEJCjUXZQd8fHBByX075/CvHkOCgpsTJ9eSlaWyqYTSUSTMNM0FwOL9xl+co/jBcDFkYxBJJZWrrRy6aWp/PGHldGjy7jhBg+gLYZEpGrNmgXIyyvloYecPP64i/POS2P8+DIuvVTdXROF2kGI1LKd3e0PPiSdpv/uxL/+eJXx43cnYKAthkSkeux2uO++cmbOLMVuh1tuSeX221243bGOTGqDkjCRWrSzu729YBVWv49j/SuYw+Xc0HD2XudpiyERqYnzz/ey/I7nWeNqx7QX0ihtfRplM1+PdVhygGJ9d6RIQqlJd3ttMSQi1eXKz6PVfbvvomxVugLuuIav/4TDhqqqp67SSphILbKaKrgXkdoX7gOeddyjzJmj9ZS6SkmYSC1Zu9ZKgSUr5DEV3IvIgQj3Qa5NYDW33ZbKPfe48HhCniJxTEmYSC346ScLPXum8qDv7pDHVXAvIgci3Ae58mMyycz08eyzTi67LJU//4xgV1epdUrCRA7Qr79a6Nkzjd9/t3LsAxep4F5Eal24O6p9w4Ywf34J553nYckSO+eck8bKlXprryt0IVnkAGzeHEzAfv7Zyp13urnxRg9uVHAvIrXLndOTIqi4fVlOT+oDM2aUkZvrZ/x4FxdckMbkyWVceKH6icU7JWEi+6mwEC65JJUffrBy661uhgwpj3VIIpLAKruj2mqFYcPKOfZYPwMGpHD99amsXOnmrrvKsdmiHKhUm9YsRfbDtm3Qq1caBQU2rr22nHvvLY/oBrsiItVx/vleFiwo4aij/Eye7KJPn1S2b491VBKOkjCRGiouhiuuSOWrr2xcfrmHMWPcSsBEJG5kZvr55Nbn+b7eccx7L4XyNqex/Tk1do1HuhwpUgNlZdC3byqffWbnoos8TJxYhlUfZUQkjrjy88gYsruxq+FeAXdfw9d/q7FrvNHiUfxbAAAgAElEQVTbh0g1eTxwww0pLF5s59xzPTz5ZJlqLUQk7lTW2DU/X2sv8URJmEg1BAJw++0pLFzoIDvbyzPPlOFwxDoqEZGKKmvs2r9/KuPHOwkEohyUhKQkTKQaxo1zMnu2gxNP9DFzZikpKbGOSEQktHCNXd3/l0nLlsE2FjfdlEJZWZQDkwqUhIlU4cUXHeTmurilycssLT6eI45JJz27E678vFiHJiJSQbjGrv47hrBgQQmnnOLjjTcc5OSksXmz7iqKJSVhIpV4/30bd9zh4rr6L/P4H1eSsnYVFp8Pe8EqGvbvp0RMROKOO6dn2J07MjICvP56CT17eli+3Ma556axYkWsI05eSsJEwvjqKyvXX5+K0wkTm4wNeU7a5IlRjkpEpGrunJ4ULlrKH7/9ReGipXs1eU1JgSefLOOuu9xs2GDl1FODHzgl+pSEiYSwbp2FK69MpawMnnmmlPq/hC50DVcAKyISzywWGDKknOeeK8Xrhd69U5k2TXcbRZuSMJF9bNkS7Ib/xx9WHnnEzTnn+MIWuoYbFxGpC7p397J4MTRuHGD48BRGjnTh98c6quShJExkDyUl0K0brFtnZdAgN336eILjYQpdSwYOiWZ4IiK1ypWfR/vr2rG50EmBsx1/TnmDG27QnZPRoiRMZAevF268MYXPPoNLL/UwfPjuDbkrK3QVEamLXPl5NOzfD1aswOLzkVm+gjlcTurbr9OzZyp//RXrCBOfWueKEGzGOny4i4ULHZx9NkycWFZhP0h3Tk8lXSKSMMJ11n+o4ViO/rwXXbvW4+WXSzjqKHV2jRSthIkAkyc7ef55J23b+sjLA6cz1hGJiERWuBuLjiwp4JZb3Pzwg5WuXdNYvlypQqTob1aS3muv2Rk71kWLFn5efrmUhg1jHZGISORVdsPRiBHlPPJIGX/9ZaFHjzQWLNCFs0hQEiZJ7YsvrAwenEKjRgHmzCnlkEO07C4iyaGqG46uucbDCy+UYrFA374pPPecWljUNiVhkrR+/dVC376p+Hzw7LOltG6t+7JFJHnsvOGIdu3C3nDUpYuPN98soUmTAHffncKIEWphUZu0vihJqbgYrr46lS1brIwdW8YZZ/hiHZKISNS5c3rCDdfwx5ZtYc854QQ/CxaUcPnlqUyd6mTjRgtPPFGGyxXFQBOUVsIk6QQCMHBgCitW2Ojdu5xrr/XEOiQRkbjWsmWAefNK6NDBy1tvObjiilS2hc/bpJqUhEnSyc118vbbDjp18vLQQ+4KrShERKSiZv/J4+O/T8BrsfPEf//BU9nvsGmT/gM9EErCJKm8846dceNctGzpZ9q0MrWiEBGphp2NXZ1rVmEL+GjHCsZvuJKpZ7zNjz8qEdtfSsIkaaxYYeXWW1OoVy/ACy+U0qRJAFd+HunZnWjSPJ307E648vNiHaaISNwJ19j1+j8foWvXNL76SunE/tDfmiSFzZstXH11KqWlMGVKGVlZ/l2f7OwFq7D4fNgLVgW38JgzJ9bhiojElXCNXdtaV1NYaCEnJ42PPrJFOaq6T0mYJDy3G665JpVff7UyfHg5553nBcJ/suOhh6IYnYhI/AvX2DWQmcm0aWX4fHDVVank5anpQk0oCZOEFgjAHXek8MUXNnr08DBw4O5NucN9smP16ihFJyJSN1TW2LVrVy+vvVZKvXpw882pTJmipq7VpSRMEtrUqQ5mz3Zw4ok+Hn107025w32yIysrOsGJiNQROxu7erPahmzs2rGjj7ffLqF5cz8jR6qpa3UpCZOE9eGHNkaNctGsmZ+ZM0tJTd37eLhPdgwfHvngRETqGHdOTwoXLeWP3/6icNHSvTrrA7Rp42fevBJatfIxdaqTAQNS8KgNY6WUhElC+vFHC/37p+JwwPPPl9K8ecU9IcN9sqNXrxhELCJS97VoEeCdd0o46SQfr7/uoG/f4A1REpoq6CThlJRAv36pFBVZePzxUv7xj/Br4u6cnhU+zYmIyP5r3Bjy8kq45ppU3n/fzmWXpTJrVikNG8Y6svijlTBJKIEA3HlnCqtX2+jTp5zLLvPGOiQRkaTiys+jxfmd+Oi/KaxreBxH/C+Piy5KY/NmNXXdl5IwSSizZjl45RUHJ5zgY/Rod6zDERFJKvv2XzyyaCVzuJxjV75Gt25p/PyzErE9KQmThPH111aGD3eRnh5g2rRSXK5YRyQiklzC9V/MbTKWdeusdOuWhmkq9dhJfxOSEAoL4dprU/F44KmnSjn88IqF+CIiElnh+i8eurWAkSPL2LjRSvfuaXz5pdIPiHBhvmEYhwCjgeNN0zwlxPGRwNnAzptYWwNXmKa5KJJxSWLx+4MNAn/5xcqwYW7OOssX65BERJKSr3Um9oJVIcdvvtlDenqAwYNT6NEjjeefLyU7O7n/v450KtoZeAsIdxF4GdDFNM0zgLOAb4HFEY5JEsyjjzr58EM7Z53lZejQ8qofICIiEVFZZ32Ayy/3Mm1aGV4vXHllKnPnJneThogmYaZp5gHbKjk+1zTN4h1fXgjMNU1T15Gk2v7zHxvjxjlp0cLPlCmlWLXCLSISM1V11gfo2tXLyy+X4nDAddelMGtW8m5zZAkEIpvzGIZxBjDBNM2TqzjvLeBK0zS3V/WcXq8vYLdrt/Zk9/PP8I9/wLZtsGQJnFLhgreIiMSrL76A886DP/+E3FwYMiTWEUVUyCuCcbEOaBjGCcDa6iRgAIWFJRGOCDIyGrBlS9hFvIRWF+budkNOThp//mlj/PgyjjzSw5Ytu4+78vNIm5SLbe0afK0zKRk0tNpNWevC/CMlmecOyT1/zT055w6xm/+RR8Kbb1q55JJUhg618vvvbm6/vXyvPX4jLVpzz8hoEHI86hdvDMOoZxhGxj7DtwJPRDsWqbtGjHDx5Zc2Lr3Uw9VX77052b59auwFq2jYvx+u/LwYRSsiIvty5efR8YYO/LbFyWpHO34en8/IkS4ifIEurkQ0CTMMIxvoDTQ3DONewzBSgb7Ag3uc0wxwmaa5PpKxSOJ47TU7M2Y4adPGx7hxZRU+NYXrU5M2eWIUohMRkars+2G5jWcFc7icv556g9tvd+FLkpsmI3o50jTNxVS82/HJfc7ZBFwVyTgkcaxZY+X221No0CDAjBmlpKVVPCdcn5pw4yIiEl3hPiyPSnmIzBd7UVxs4fHHy3AkeM2+7iWTOqO0FG64IYXSUguPPVbG0UeHXrP2tc6s0biIiERXuA/Frb2rOflkH2+84eDaa1NwJ/juc0rCpM64/34Xa9bY6NevnK5dw2/MXVWfGhERia3KPiy/+moJp5/uZeFCB1ddlUpxcchTE4KSMKkT5s61M3NmsA5s5MjKPxpVp0+NiIjETmUfluvXh5deKuWcc7wsXmynV69UioqiHGCUxEWLCpHKbNhgYfDgFFJTAzzzTBkpKVU/xp3TU0mXiEiccuf0pIjgDVO7WgkNHLLr/+2UFJg+vZRbbkkhP9/BxRenMWdOKQcfnFi3TioJk7jm9cLNN6fw998WcnPLMAx/rEMSEZFaUNWHZYcDpkwpo169ALNmObnoolRee62UQw5JnERMlyMlrk2c6OR//7PTvbuHq67yVP0AERFJGDYb5Oa66d+/HNO0ceGFaWzYEMVurhGmJEzi1qef2pg40cnhh/vJza3YD0xERBKfxQIPPOBmyBA369ZZufDCNH76KTHeEJSESVwqLISbbkrBYoGnniqlUaNYRyQiIrGS8mYejyw4Ca/FztxfTmB6l7f5/vu6n4gpCZO4EwjA4MEp/PablWHDymnfXnVgIiLJas/u+raAj3as4KmtVzLjnLcpKKjbaUzdjl4S0syZDubPd3DaaV4GDiyPdTgiIhJD4brrD9j2CDk5qaxYUXdTmbobuSSk1autjBjhIj09wJQpZdhssY5IRERiKVx3/bbW1RQWWujRI43ly+tmOlM3o5aEVFICN96YgtttYfLkUpo3T5zbkEVEZP+E664fyMxkypQytm+Hnj3T+N//6t6ndiVhEjdGjAhuS3TddeWce64v5Dmu/DzSszvRpHk66dmdcOXnRTlKERGJpsq66198sZdnnimjvBx69Url44/rViKmJEziwty5dl54wUlWlo8RI0JvS7RncabF58NesIqG/fspERMRSWBVbUXXrZuXGTNK8XrhyitT+eCDupOIKQmTmNu0ycLQoVVvSxSuODNt8sQIRiciIrHmzulJ4aKl/PHbXxQuWlqh036XLj5mzSrFaoU+fVKZN69ubAikJExiamc7isJCC/ff76Z16/DtKMIVZ4YbFxGR5HHGGT5mzy7F6YTrrkvh7bfjPxFTEiYxNWuWgw8+sJOd7eWaayrflihccWa4cRERSS5nbnqF3zKOo8zn4JTrOvDN8PxYh1QpJWESMz/9ZOG++1w0ahRg8uSqtyWqrDhTRESS28664YY/rcJOsKnrv6f14cs74jcRUxImMeHzwa23plBSYuHhh8s49NCq21FUVZwpIiLJK1zd8CEzc5k9Oz4vTcZnVJLwnnrKwWef2ene3UOPHt5qP86d01NJl4iIVBCuPjiL1ZwwMBWvt4zevSsve4k2rYRJ1K1ebeXhh100bernkUfcVV6GFBERqUq4+mD30ZkcfLCfoUNTmD7dEeWoKqckTKKqvBwGDEihvNzCo4+WcfDB6oovIiIHLlzdsP/OIeTnl5KR4eeuu1J49tn4ScSUhElUTZjgZNUqG717l3P22aG74ouIiNRUZXXDmZl+3nyzlGbN/NxzTwpTpsRHIqaaMImaL76w8thjTlq29DNqVOiu+CIiIvursrrhVq38vPVWCTk5aYwcmYLXa+HBB6Mc4D60EiZRUVwMt9ySSiAAjz9eRv36sY5IRESSzdFHB3jzzRJatPAzerSL0aNjG4+SMImKBx5wsW6dlZtu8tCpky5DiohIbBx1VDARa9nSz4gRsG1b7GJREiYR99FHNmbMcJKZ6eOuu3QZUkREYqvV8tcwU9rhtdhpeUEnXPl5MYlDSZhE1NatMGhQCnZ7gCefDL05tys/j/TsTjRpnk56duz+MYiISOLb2Vk/Ze0qrH4f9oJVNOzfLybvPdUqzDcMIwU4GsgAtgLrTNMsimRgkhjuuiuF33+3Mny4m+OOq7g5985/DDvt/MdQBGrKKiIitS5cZ/20yROj/r5T6UqYYRjphmHMADYDS4AXgQ+AjYZhzDMMo3UUYpQ6av58O2+84eCkk3zcemt5yHMq+8cgIiJS28J11g83HklhkzDDMBoCs4C3gMNM02xsmmZL0zQzgHTgEWC8YRhZ0QlV6pKtW+GOO1w4ncHNue1h1lzj6R+DiIgkvnCd9cONR1JlK2EtgatN03zTNM297h0wTbPcNM2PgYsJJmQiexk50sXmzVZuv72c1q0rXobcKZ7+MYiISOIL11m/ZOCQKEdSSRJmmuZK0zT/BDAMo92+xw3DuNg0Ta9pmp9EMkCpexYtsvHyy07atvUxYEDoy5A7xdM/BhERSXx7dtZnn8760VbduyMfMwyjwc4vDMM4BXg4MiFJXbZ9OwwdmoLNFrwM6ahiZ4jKtpkQERGJBHdOTwoXLQWPh8JFS2P2nlPdbYu+AyYZhvEKcBrQF/gtUkFJ3TV2rItffrEycGDouyFDqWybCRERkURV3SRsBMH2FB8TbFFxErA9UkFJ3fTZZzamTXPQqpWPoUMrvwwpIiKS7KqbhC0C6gE3AiYwDnABV0YmLKlryspg8GAXAI8+Gropq4iIiOxW3STsbyDbNM3fAQzDuJlg6woRAHJznXz/vY3rry+nffvqXYYUERFJZtUtzL95ZwIGYJpmGTAgMiFJXfPtt1aeeMJJy5Z+hg/X3pAiIiLVUVmz1lMNw+gEYJrmsn2Pm6b5vWEYhxmGcUkkA5T45vEE94b0+SxMmFBG/fqxjkhERKRuCHs50jTNpYZhvGAYxtXA+8DPQDGQAhwCdAbaE2zYKknqiSecrFxp44oryjnjDF+swxEREakzqqoJKwY+Ba4H2gFNCNaHfQe8BlxgmqauPyWptWut5OY6adbMz6hR+jEQERGpiaqSsDLTNF8wDKOdaZrn7XnAMIwrlIAlL58veBmyvNzCuHFlNGoU64hERETqlqqSMMMwjH5Aux2XJfd0FfByZMKSeDdtmoNly2xcdJGH887zhjzHlZ9H2qRcbGvX4GudScmgoWrKKiIiskNVSdhY4GqgBXDmPscOq+rJDcM4BBgNHG+a5ilhzukDHLzj1/GmaV5Q1fNKbK1fb2HsWBeNG/sZMyb0YqgrP4+G/fvt+tpesIqG/ftRBErEREREqCIJM01zCbDEMIwepmm+secxwzB6VOP5OxPsJ3ZCqIOGYXQGjjBN84EdX1fYKFziSyAAd96ZQklJ8G7IjIxAyPPSJuWGHp88UUmYiIgI1ewTtm8CFm4sxDl5wLZKTrkKsBqGMdAwjLGArTrxSOy8846djz6yk53t5eKLQ1+GBLCtXVOjcRERkWRjCQRCr2TUFsMwzgAmmKZ5cohjC4CNpmn2MwyjMfAlcKJpmoWVPafX6wvY7crXou3vv6FNG/jrL1i5Eo45ppKT27WDFStCj3/zTcRiFBERiUOWUIPV3bYoUoqAzwBM0/zLMIzfgeMJ7lUZVmFhScQDy8howJYtlS3iJa5wcx8+3MXGjU7uvNNNo0blbNkS/jlctwzeqyZsp6IBg3DH+d+rvvfJOXdI7vlr7sk5d0ju+Udr7hkZDUKOV3fbolpjGEY9wzAydnz5IXD0jnErwSawP0Y7Jqna119bmT7dwTHH+LjllvIqz3fn9KTo6el4s9oSsNvxZrWl6OnpqgcTERHZIaIrYYZhZAO9geaGYdwL5AJ9geOAG4GZwCM7jh0GjDRN8+dIxiQ15/XC7benEAhYGD/ejctVvce5c3oq6RIREQkjokmYaZqLgcX7DD+5x/FyYHAkY5ADN326g2+/tXHppR5OO01bE4mIiNSGqF+OlLpl40YLDz3kIj09wMiR2iBBRESktsS6MF/i3D33uCgutjB6dBlNmkT2TloREZFkopUwCev9923MneugfXsvl1/uiXU4IiIiCUVJmIRUUgJ33ZWC3R5gwgQ3Vv2kiIiI1Cq9tUpIublOfvnFys03l5OZ6Y91OCIiIglHSZhUsHIlPPWUk5Yt/QwZUnVPMBEREak5JWGyF78f+vcHr9fCww+XkZYW64hEREQSk5Iw2cvLLztYuhS6dfPw739X7Anmys8jPbsTTZqnk57dCVd+XgyiFBERqfvUokJ22bLFwgMPuGjQAEaPrtgTzJWft9d+kPaCVTTs348iUGd8ERGRGtJKmOwyapSLrVstjB4NzZtX7AmWNik35OPSJk+MdGgiIiIJR0mYAPD551ZefdXBccf5GDAg9Dm2tWtqNC4iIiLhKQkTfD4YPjwFgIceKsNmC3Ne68wajYuIiEh4SsKEF190sGJFcIPu9u3D9wQrGTQ09PjAIZEKTUREJGEpCUtyf/0FDz3kon79APfdV/kG3e6cnhQ9PR1vVlsCdjverLYUPT1dRfkiIiL7QXdHJrmHH3ZRWGhh1KgymjWreoNud05PJV0iIiK1QCthSWzFCivPP++gdWsf112nDbpFRESiSUlYkgoEYPhwF4GAhTFj3DgcsY5IREQkuSgJS1J5eXY+/9zOBRd4yM6u2BlfREREIktJWBLati3YmDU1NcCoUZUX44uIiEhkKAlLQrm5LjZvtnLrreUcfnjVxfgiIiJS+5SEJZnvvrPyzDMOWrb0M2BAeazDERERSVpKwpJIIAB33+3C67Xw4INuUlNjHZGIiEjyUhKWRObPt7N4sZ0zz/Ry7rneWIcjIiKS1JSEJYnSUrj/fhcOR4AxY8qwWPY+7srPIz27E02ap0O7drjy82ITqIiISJJQx/wk8cQTTn7+2cott7g55pi9i/Fd+Xk07N9v98CKFTTs348iUHd8ERGRCNFKWBL4+WcLjz/upFkzP0OGVCzGT5uUG/JxaZMnRjo0ERGRpKWVsCQwYoSLsjILjz5aRv36FY/b1q4J+bhw4yIiInLgtBKW4P77Xxvz5zvo2NFLjx6hi/F9rTNrNC4iIiIHTklYAvP54L77XFgsAUaPdlcoxt+pZNDQ0OMDh0QwOhERkeSmJCyBzZ7tYPVqG5dd5qVdO3/Y89w5PSl6ejrerLYE7HZo146ip6erKF9ERCSCVBOWoLZvh4cecpKWFuDuu6veH9Kd03NX0pWR0QD3lm2RDlFERCSpaSUsQU2e7GTLluD+kIccov0hRURE4o2SsAT0yy8Wpk51cuihfm66SftDioiIxCMlYQlo9GgXbreFe+5xk5YW62hEREQkFCVhCeaLL6zk5zs48UQfF1+s/SFFRETilZKwBOL3w4gRKQA88IAbq767IiIicUtv0wkkP9/O8uU2LrzQQ4cOvliHIyIiIpVQEpYgSkqCtWAuV4D77qu6JYWIiIjElpKwBDF1qpNff7Vyww3ltGy5uyWFKz+P9OxONGmeTnp2J1z5eTGMUkRERHZSs9YEsGmThccec9KkiZ9Bg3a3pHDl59Gwf79dX9sLVtGwfz+KQN3wRUREYkwrYQngoYeclJRYuOuucho02D2eNik35PlpkydGKTIREREJR0lYHbdihZXZsx20aePjyis9ex2zrV0T8jHhxkVERCR6lITVYYEAjBjhIhCw8MADbmy2vY/7WmeGfFy4cREREYmeiNaEGYZxCDAaON40zVNCHD8DmARs3TE0zzTN8ZGMKZEsWGDnk0/snH22l+zsii0pSgYN3asmbNf4wCHRCE9EREQqEenC/M7AW8AJlZwzyDTNRRGOI+GUl8OoUS7s9gAjR4ZuSeHO6UkRwRow29o1+FpnUjJwiIryRURE4kBEkzDTNPN2rHZVprdhGCcDDYFnTdP8JZIxJYoZMxysW2fluuvKadXKH/Y8d05PJV0iIiJxyBIIBKo+6wDsSMImmKZ5cohjTYE00zR/MgzjWOB1IMs0zfBZBeD1+gJ2u62yUxLa33/D0UeDzwc//AAHHxzriERERKQSllCDMe0TZprm5j3+vMowjIOAw4H1lT2usLAk0qGRkdGALVu2Rfx19seYMU7++svFvfe68fvL2bKldp8/nuceDck8/2SeOyT3/DX35Jw7JPf8ozX3jIwGIcejfnekYRj1DMPI2PHnuwzDaLzjz40BJ7Ap2jHVJRs3WnjmGSfNm/u57rryqh8gIiIicSnSd0dmA72B5oZh3AvkAn2B44AbgZ+AyYZhrAaygN6maZZFMqa6btw4J6WlFsaOdZOWFutoREREZH9FujB/MbB4n+En9zg+B5gTyRgSiWkGG7Maho/LLvNU/QARERGJW2rWWoeMHu3C77dw771u7Nr1U0REpE5TElZH/O9/Nt59107Hjl66dKnYmFVERETqFiVhdUAgEGzMCjBihBtLyBtdRUREpC5RElYHzJtnZ/lyG127ejj5ZD+u/DzSszvRpHk66dmdcOXnxTpEERERqSFVFsU5jwfGjHFhswW45x43rvy8vfaDtBesomH/fhSBOuOLiIjUIVoJi3MvveTghx+sXHWVh2OOCZA2KTfkeWmTJ0Y5MhERETkQSsLi2PbtMH68k7S0ALffHmzMalu7JuS54cZFREQkPikJi2NPP+1kyxYrN91UTrNmwT0+fa0zQ54bblxERETik5KwOLVli4UnnnDSpImfAQN2b09UMmhoyPNLBg6JVmgiIiJSC5SExamJE50UF1sYOrSc+vV3j7tzelL09HS8WW0J2O14s9pS9PR0FeWLiIjUMbo7Mg79+KOF5593cOSRfnr3rrg9kTunp5IuERGROk4rYXHooYdceL0W7rnHjdMZ62hEREQkEpSExZmvvrLy1lsOTjzRR/fu3liHIyIiIhGiJCyOBALw4IPankhERCQZKAmLIx9/bGPJEjtnneXltNO0SbeIiEgiUxIWJwKBYC0YwPDh7hhHIyIiIpGmJCxOLFxo58svbVxwgYfjj/fHOhwRERGJMCVhccDvh4cfdmK1BrjzzvKqHyAiIiJ1npKwOJCfb6egwEbPnl4MQ6tgIiIiyUBJWIx5PDBunAuHI8DY418iPbsTTZqnk57dCVd+XqzDExERkQhRx/wYmzPHwbp1Vqb8cxb/d881u8btBato2L8fRaDu+CIiIglIK2ExVFYGublOUlIC9N34cMhz0iZPjHJUIiIiEg1KwmLo+ecd/PablX79PKT8uCbkOba1ocdFRESkblMSFiPbt8PkyU7q1w9w663l+Fpnhjwv3LiIiIjUbUrCYuTZZ5388YeVG28s5+CDA5QMGhryvJKBQ6IcmYiIiESDkrAY2LoVnnzSSXp6gJtuCvYFc+f0pOjp6Xiz2hKw2/FmtaXo6ekqyhcREUlQujsyBp580klRkYURI8po0GD3uDunp5IuERGRJKGVsCjbvNnCs886adbMT79+nliHIyIiIjGiJCzKJk92UlJiYfDgctLSYh2NiIiIxIqSsCjasMHC8887aNnSz1VXaRVMREQkmSkJi6LcXCfl5RZuv92N0xnraERERCSWlIRFyQ8/WJgzx0Hr1j4uucQb63BEREQkxpSERcm4cS58Pgt33lmOzRbraERERCTWlIRFwerVVvLzHbRr56NrV62CiYiIiJKwqJgwIVgAduedbqz6GxcRERGUhEXcypVW6s19nbUp7bj86oakZ3fClZ8X67BEREQkxtQxP8K+GJrPHHpDWfBre8EqGvbvRxGoO76IiEgS00pYBK1YYeXcr8aFPJY2eWKUoxEREZF4oiQsgnJznWSxOuQx29o1UY5GRERE4omSsAhZscLK/PkO1qVmhTzua50Z5YhEREQknigJi5Cdd0RuuX5oyOMlA4dEMxwRERGJM0rCImDFCisLFjg4+W90d5oAAAw4SURBVGQfx9zTg6Knp+PNakvAbseb1Zaip6erKF9ERCTJ6e7ICBg/PrgKNmyYG4sleBekki4RERHZU0STMMMwDgFGA8ebpnlKJedlAx8CJ5imuTKSMUXat99aWbjQwSmn+DjjDF+swxEREZE4FenLkZ2BtwBLuBMMw2gKXAZsiHAsUTF+vAuAO+4IroKJiIiIhBLRJMw0zTxgW7jjhmFYgbHAPZGMI1q++cbKu+/aad/eyz//qVUwERERCS/WNWF3Ac+aplloGEa1H5SenobdbotcVDtkZDSo0fmTJwd/HzvWTtOmNXtsvKnp3BNNMs8/mecOyT1/zT15JfP8Yzn3mCVhhmGkAG0Bv2EYZwKNgGsNw5hrmuaHlT22sLAk4vFlZDRgy5awi3gVfPWVlblz69Gxo5fjjitly5YIBhdhNZ17oknm+Sfz3CG556+5J+fcIbnnH625h0v0op6EGYZRD0gzTXMLcMUe4zcC0+pqYf6ECcFasGHDylULJiIiIlWKaE3YjrseewPNDcO41zCMVKAv8OAe5zgMw7iX4ErYDYZhhG4xH8e+/NLK++/b6dTJS+fOqgUTERGRqkV0Jcw0zcXA4n2Gn9znHA/BNhajIxlLJO1cBbvjDq2CiYiISPWoY/4BWr7cygcf2Dn1VC+nnaZVMBEREakeJWH7yZWfR3p2J84+vxHf0I5JHV+KdUgiIiJSh8S6RUWd5MrPo2H/fru+bscKmNiXIsOv7YlERESkWrQSth/SJuWGHp88McqRiIiISF2lJGw/2NauqdG4iIiIyL6UhO0HX+vM/2/v7mPkKqsAjD9btttCdaNNqATEL5ADpRUEvwgqEkTAxki1ILGAUAg0irZW1IqKKApICwGsYoFWgwryoUCgKhgJaBQUMBoCetBKxQhKBbRYaLcf6x/3Dl7XbXfa7u5lZp5f0jT3fe805/TMnTn3nXtntmhckiRpIJuwrfDHo08fdPyZOfNGORJJktSqbMK2wqfvn8kxXM1TL5tCf3c36ydPYdXipV6UL0mSmubdkVto+fIubryxm732Pop1t0/jH345qyRJ2gquhG2hSy4Zx8aNXcyb57fjS5KkrWcTtgUeeaSL667rZo89NjBt2vq6w5EkSS3MJmwLLFrUw/r1Xcyd28cY/+ckSdI2sJVo0mOPdXHVVWN5xSs2cuSRroJJkqRtYxPWpK99rYe+vi7mzOmj29sZJEnSNrIJa8LKlV1ceeVYdtllI0cdta7ucCRJUhuwCWvC4sVjefbZLk47rY+enrqjkSRJ7cAmbAhPPQVLlvQwadJGZs50FUySJA0Pm7AhXHFFD6tXd/GhD/Uxfnzd0UiSpHZhE7YZTz8Nl13Ww8SJGzn+eFfBJEnS8LEJ24xvfKOHf/2ri9mz1zFhQt3RSJKkdmITtgmrV8Oll46lt7efWbP66g5HkiS1GZuwTbj8cnjiiTGcfHIfvb11RyNJktqNTdgg1qyBBQtgwoR+TjnFVTBJkjT8bMIGcfXVY3n0UTjxxD4mTqw7GkmS1I5swgZx7bVjGT8eZs/2jkhJkjQy/BXEQcyfv5be3h2YNKm/7lAkSVKbciVsgHE3XM+RZ76Bd7yzmxcfdADjbri+7pAkSVIbciWsYtwN19N76qzntrt/9wC9p85iFbB2+oz6ApMkSW3HlbCKHS66YPDxiy8c5UgkSVK7swmr2O6h32/RuCRJ0tayCavYsMeeWzQuSZK0tWzCKp6Z+7HBx+fMG+VIJElSu7MJq1g7fQarFi9l/eQp0N3N+slTWLV4qRflS5KkYefdkQOsnT6DtdNnsOOOL+SplU/XHY4kSWpTroRJkiTVwCZMkiSpBjZhkiRJNbAJkyRJqoFNmCRJUg1swiRJkmpgEyZJklQDmzBJkqQa2IRJkiTVwCZMkiSpBl39/f11xyBJktRxXAmTJEmqgU2YJElSDWzCJEmSamATJkmSVAObMEmSpBrYhEmSJNWgu+4ARltE7AR8EdgnM18/yPwY4Bzg38DLgSWZeXc593bgPcDjQH9mfn7UAh8mTeR/AvAmYDmwH/CVzPxFOXc3sKbcdUNmHjIqQQ+TJnJ/G3AR8M9yaFlmLijnWrr2TeR+FnAosK4c2gN4f2be0QZ1340i918DLwWeyMwvDNhnPLAQ+CvwauC8zHyonDsWeC2wAViemYtHMfxt1mT+nwR2Av4G7A+cmZm/L+dWACvKXf+amTNHJfBh0GTuJwCz+e9zfElmfquca9naN5n7EmC3ytBrgP0yc0Ur1x2eey+/Gfgl0EOR56zMfLayT+3Hfcc1YcCbgZuAfTcxfzTQm5nzI2IicHdE7AWMA74O7J2ZayPiexFxSGb+ZHTCHjZD5b8LMDcz10TEG4ErgKnl3I8y86yRD3HEDJU7FLnfUR2IiB1o/doPlfu9wILMXF2+eP0AuLOca/W6TwS+m5k3AUTEgxGxLDPvq+wzF3gkM8+PiKnAEuAtEfFS4HTgtZnZHxH3RMTtmfmHUc9i6zWT/wuAeWWO7wMWAO8q577ZwvVvJneAYzJzRXWgDWrfTO63ZeY15XwvRa1XlHOtXPeGuzLziwARcRPFifR3KvO1H/cd14Rl5vXlisemTANuK/d9MiLWAHsDOwJ/zsy15X4/L/dtpTfiIfPPzC9VNsdQrAg2TC3PmLcH7snMZSMT5choovYAx0XE64Be4PLM/AtwAC1e+ybqfktl893ALZnZ+CbnVq/7PQOGxgCrB4xNA84o978/IvYp35QOA+6r/F/cBRwBtMobcVP5Z+ZnB8xXj/u3RsQngBcCP2ysjLeCJmsPcFpE/A3YAViUmU/S4rVvsu7XVDZPApZWtlu27gCZuZFiJZCI6KZYDcwBu9V+3HtN2P+bBDxd2V5Vjm1qvC1FRBcwB5hXGf5yZn4ZOBs4IyLeWktwI+dB4OzMXAhcA/y4XBXqqNoDJwDfrGy3Td0jYjpwa+OjtoqOOO43k39jvgf4APCZyvD8zDwfOBdYGhG7j3ykw28zud9J8RxfSLEifF053ja1b6LuYygaj+oJVrvU/TDgFooTy3sHTNd+3NuE/b/HKTr/ht5ybFPjbadswBZQLEff1RjPzF+Vf28AfgYcXE+EIyMzH28sxWfmA8CLgF3prNrvCzyUmc+thLRL3SPiYIrYPzrIdNsf90Pk32jALgU+nZnLG+OV+j8D/AY4cOSjHV6byz0zH87MleXm7cBBEbEdbVL7oepeGrj63RZ1B8jMWzPzcOCVEfHBAdO1H/c2YUBETIiIHcvNZRQfP1FeEzYeeIBiOfLlETGu3O9A/vesoWVV8y9ffC4Gbs7MH0XEe8vxPSPipMrDXg38cfSjHV4Dcm9cB9iofQ/wd9q09gOe9w0fBhZV9mmLukfENIoz/TnAThFxQERMLD96gP897qcCv83MVcCtwP7liQnlPj8c3ei33VD5R8T2wGLgwsy8r3LcHxIRh1f+qd0pbtppGU3kfm75cRUUz++HyxOOlq99E8/7hhOorH63Sd0nl/k3PAy86vl23HfcD3hHxEHA8cDhFGd9FwCzgKmZObtclj0XeAZ4GcV1QY27Iw8FZgArgXWtdoccNJX/hRQ5/ql8yG6ZuWtE7Ax8leJOm15gLMWFvBtHO4et1UTux1BcI/AgMJniotZl5WNbuvZD5V7u8xLggsw8tvK4dqj7/hQfOTU+iphAkdNk4MnMPK9sQhYCj1G84Zwz4C6p11HcJfVQK90hB03n/31gCvBoY5/MfH35xnQWcB+wM8VdcueOZvzbosnc51Dk/jDFTUgXV17zW7b2zeRe7rcvMDMzP155bEvXHZ67O3QBxWvXWGAv4CMUl9g8b477jmvCJEmSng/8OFKSJKkGNmGSJEk1sAmTJEmqgU2YJElSDWzCJEmSamATJkmSVAObMEmSpBp03A94S1JVRJwNfKr881Pg2xQ/2fWlzT5QkraRX9YqqeNFxHkUv5BxGbBPZl5cc0iSOoArYZIEZ1L8vMt84IiaY5HUIbwmTFLHy8w+4FcUvx04qeZwJHUImzBJHS8ijgNuBhYBl9ccjqQOYRMmqaNFxBzgc8ATwHLgiIi4OiIm1BuZpHbnhfmSJEk1cCVMkiSpBjZhkiRJNbAJkyRJqoFNmCRJUg1swiRJkmpgEyZJklQDmzBJkqQa2IRJkiTV4D+UonVk3hQBlQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([xd, xd], [f(xd), iyd], ['b', 'ro'],\n",
    "            ['f(x)', 'interpolation'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_12.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "uuid": "c3d9f85f-671f-4353-beab-fad9db9f8aa4"
   },
   "outputs": [],
   "source": [
    "ipo = spi.splrep(x, f(x), k=3)  \n",
    "iyd = spi.splev(xd, ipo)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "uuid": "8c67b514-160e-40e3-8f69-da81d7579b2d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(f(xd), iyd)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "uuid": "ecc6c2fb-faa4-4149-b71e-05ac5cddeb79"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1349319851436892e-08"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean((f(xd) - iyd) ** 2)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "uuid": "0c3e96f1-8732-4ce6-a6ed-bbaae732d950"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([xd, xd], [f(xd), iyd], ['b', 'ro'],\n",
    "            ['f(x)', 'interpolation'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_13.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convex Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "uuid": "a09a918e-760c-4e9c-95b8-fe3b568dacdb"
   },
   "outputs": [],
   "source": [
    "def fm(p):\n",
    "    x, y = p\n",
    "    return (np.sin(x) + 0.05 * x ** 2\n",
    "          + np.sin(y) + 0.05 * y ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "uuid": "1f4a147b-d9d2-42d5-8553-dd95d75d8251"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-10, 10, 50)\n",
    "y = np.linspace(-10, 10, 50)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z = fm((X, Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "uuid": "b3a1d3b7-25eb-4ac8-81ed-ad740fd1a297"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0xb1ac9c2e8>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.gca(projection='3d')\n",
    "surf = ax.plot_surface(X, Y, Z, rstride=2, cstride=2,\n",
    "                       cmap='coolwarm', linewidth=0.5,\n",
    "                       antialiased=True)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('f(x, y)')\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "# plt.savefig('../../images/ch11/math_14.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Global Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "uuid": "72b2e44d-2127-412e-9046-2b0c7c5bf7c6"
   },
   "outputs": [],
   "source": [
    "import scipy.optimize as sco  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "uuid": "e6c829bb-f358-430d-9e8c-781e9d15c9e6"
   },
   "outputs": [],
   "source": [
    "def fo(p):\n",
    "    x, y = p\n",
    "    z = np.sin(x) + 0.05 * x ** 2 + np.sin(y) + 0.05 * y ** 2\n",
    "    if output == True:\n",
    "        print('%8.4f | %8.4f | %8.4f' % (x, y, z))  \n",
    "    return z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "uuid": "d1f54d32-6cb5-4cd2-8a95-ea3b92c87266"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-10.0000 | -10.0000 |  11.0880\n",
      "-10.0000 | -10.0000 |  11.0880\n",
      "-10.0000 |  -5.0000 |   7.7529\n",
      "-10.0000 |   0.0000 |   5.5440\n",
      "-10.0000 |   5.0000 |   5.8351\n",
      "-10.0000 |  10.0000 |  10.0000\n",
      " -5.0000 | -10.0000 |   7.7529\n",
      " -5.0000 |  -5.0000 |   4.4178\n",
      " -5.0000 |   0.0000 |   2.2089\n",
      " -5.0000 |   5.0000 |   2.5000\n",
      " -5.0000 |  10.0000 |   6.6649\n",
      "  0.0000 | -10.0000 |   5.5440\n",
      "  0.0000 |  -5.0000 |   2.2089\n",
      "  0.0000 |   0.0000 |   0.0000\n",
      "  0.0000 |   5.0000 |   0.2911\n",
      "  0.0000 |  10.0000 |   4.4560\n",
      "  5.0000 | -10.0000 |   5.8351\n",
      "  5.0000 |  -5.0000 |   2.5000\n",
      "  5.0000 |   0.0000 |   0.2911\n",
      "  5.0000 |   5.0000 |   0.5822\n",
      "  5.0000 |  10.0000 |   4.7471\n",
      " 10.0000 | -10.0000 |  10.0000\n",
      " 10.0000 |  -5.0000 |   6.6649\n",
      " 10.0000 |   0.0000 |   4.4560\n",
      " 10.0000 |   5.0000 |   4.7471\n",
      " 10.0000 |  10.0000 |   8.9120\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0., 0.])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = True\n",
    "sco.brute(fo, ((-10, 10.1, 5), (-10, 10.1, 5)), finish=None)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "output = False\n",
    "opt1 = sco.brute(fo, ((-10, 10.1, 0.1), (-10, 10.1, 0.1)), finish=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "uuid": "dc42167b-4e8f-462c-8aad-a94afdf0a8bc"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.4, -1.4])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "uuid": "ec2669cd-36a5-4b79-a90c-761a39b12044"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.7748994599769203"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm(opt1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Local Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " -1.4000 |  -1.4000 |  -1.7749\n",
      " -1.4700 |  -1.4000 |  -1.7743\n",
      " -1.4000 |  -1.4700 |  -1.7743\n",
      " -1.3300 |  -1.4700 |  -1.7696\n",
      " -1.4350 |  -1.4175 |  -1.7756\n",
      " -1.4350 |  -1.3475 |  -1.7722\n",
      " -1.4088 |  -1.4394 |  -1.7755\n",
      " -1.4438 |  -1.4569 |  -1.7751\n",
      " -1.4328 |  -1.4427 |  -1.7756\n",
      " -1.4591 |  -1.4208 |  -1.7752\n",
      " -1.4213 |  -1.4347 |  -1.7757\n",
      " -1.4235 |  -1.4096 |  -1.7755\n",
      " -1.4305 |  -1.4344 |  -1.7757\n",
      " -1.4168 |  -1.4516 |  -1.7753\n",
      " -1.4305 |  -1.4260 |  -1.7757\n",
      " -1.4396 |  -1.4257 |  -1.7756\n",
      " -1.4259 |  -1.4325 |  -1.7757\n",
      " -1.4259 |  -1.4241 |  -1.7757\n",
      " -1.4304 |  -1.4177 |  -1.7757\n",
      " -1.4270 |  -1.4288 |  -1.7757\n",
      "Warning: Maximum number of function evaluations has been exceeded.\n"
     ]
    }
   ],
   "source": [
    "output = True\n",
    "opt2 = sco.fmin(fo, opt1, xtol=0.001, ftol=0.001,\n",
    "                maxiter=15, maxfun=20)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "uuid": "e451a278-e2ae-4d86-b357-f230468052a4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.42702972, -1.42876755])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "scrolled": true,
    "uuid": "0352d556-6ea7-47a6-9c76-e4a56c0efed7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.7757246992239009"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm(opt2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "uuid": "ff9beaf9-73d7-4157-85cb-24783abae775"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.015826\n",
      "         Iterations: 46\n",
      "         Function evaluations: 86\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([4.2710728 , 4.27106945])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = False\n",
    "sco.fmin(fo, (2.0, 2.0), maxiter=250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constrained Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "uuid": "703a8ac0-1c74-4851-9fd3-7ac404ee3446"
   },
   "outputs": [],
   "source": [
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "uuid": "703a8ac0-1c74-4851-9fd3-7ac404ee3446"
   },
   "outputs": [],
   "source": [
    "def Eu(p):  \n",
    "    s, b = p\n",
    "    return -(0.5 * math.sqrt(s * 15 + b * 5) +\n",
    "             0.5 * math.sqrt(s * 5 + b * 12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "uuid": "703a8ac0-1c74-4851-9fd3-7ac404ee3446"
   },
   "outputs": [],
   "source": [
    "cons = ({'type': 'ineq',\n",
    "         'fun': lambda p: 100 - p[0] * 10 - p[1] * 10})  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "uuid": "703a8ac0-1c74-4851-9fd3-7ac404ee3446"
   },
   "outputs": [],
   "source": [
    "bnds = ((0, 1000), (0, 1000))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "uuid": "8f989832-637a-4188-b096-26ceeabd77ea"
   },
   "outputs": [],
   "source": [
    "result = sco.minimize(Eu, [5, 5], method='SLSQP',\n",
    "                       bounds=bnds, constraints=cons)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "uuid": "67c11995-124c-4f9d-8edf-1364b412e754"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     fun: -9.700883611487832\n",
       "     jac: array([-0.48508096, -0.48489535])\n",
       " message: 'Optimization terminated successfully.'\n",
       "    nfev: 21\n",
       "     nit: 5\n",
       "    njev: 5\n",
       "  status: 0\n",
       " success: True\n",
       "       x: array([8.02547122, 1.97452878])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "uuid": "53899a89-8532-4f22-a17f-54d106412867"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([8.02547122, 1.97452878])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result['x']  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "uuid": "b8548809-fe3a-4fa4-9496-8d3b6a177973"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.700883611487832"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-result['fun']  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "uuid": "7453e87b-a70d-47b9-8a12-c5c0f01e4b86"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.99999999999999"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(result['x'], [10, 10])  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "uuid": "6a38567d-4a2d-464f-8de3-7687e1d2916d"
   },
   "outputs": [],
   "source": [
    "import scipy.integrate as sci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "uuid": "0954e5b6-9874-4bad-a2fb-28273a015e4a"
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.sin(x) + 0.5 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "uuid": "afb6151f-5743-4950-980e-18047e066ebc"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(0, 10)\n",
    "y = f(x)\n",
    "a = 0.5  \n",
    "b = 9.5  \n",
    "Ix = np.linspace(a, b)  \n",
    "Iy = f(Ix)  #  <4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "uuid": "ad78923f-e4c1-4381-9a24-33b4f1ea3c56"
   },
   "outputs": [],
   "source": [
    "from matplotlib.patches import Polygon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "uuid": "ad78923f-e4c1-4381-9a24-33b4f1ea3c56"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 6))\n",
    "plt.plot(x, y, 'b', linewidth=2)\n",
    "plt.ylim(bottom=0)\n",
    "Ix = np.linspace(a, b)\n",
    "Iy = f(Ix)\n",
    "verts = [(a, 0)] + list(zip(Ix, Iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='0.7', edgecolor='0.5')\n",
    "ax.add_patch(poly)\n",
    "plt.text(0.75 * (a + b), 1.5, r\"$\\int_a^b f(x)dx$\",\n",
    "         horizontalalignment='center', fontsize=20)\n",
    "plt.figtext(0.9, 0.075, '$x$')\n",
    "plt.figtext(0.075, 0.9, '$f(x)$')\n",
    "ax.set_xticks((a, b))\n",
    "ax.set_xticklabels(('$a$', '$b$'))\n",
    "ax.set_yticks([f(a), f(b)]);\n",
    "# plt.savefig('../../images/ch11/math_15.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numerical Integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "uuid": "6d3aa9c8-58c0-46a3-a89f-ca471a1f83e4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.366995967084602"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sci.fixed_quad(f, a, b)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "uuid": "0ddebba6-5357-4ce9-b829-d752132d12df"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.374754718086752"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sci.quad(f, a, b)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "uuid": "3b1779d6-c831-449d-964f-e2cc869847e7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.374754718086713"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sci.romberg(f, a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "uuid": "5499809d-f2b1-4cc9-8808-511f4e82c5ed"
   },
   "outputs": [],
   "source": [
    "xi = np.linspace(0.5, 9.5, 25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "uuid": "aec239bc-cdd9-4477-b47c-4d0136ed686d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.352733271544516"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sci.trapz(f(xi), xi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "uuid": "ce33e420-5143-4d54-b23f-0040f54723fc"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.37496418455075"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sci.simps(f(xi), xi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Integration by Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "uuid": "bb840eb2-0e13-40eb-aea7-0f106dcf9f41"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24.804762279331463\n",
      "26.522918898332378\n",
      "26.265547519223976\n",
      "26.02770339943824\n",
      "24.99954181440844\n",
      "23.881810141621663\n",
      "23.527912274843253\n",
      "23.507857658961207\n",
      "23.67236746066989\n",
      "23.679410416062886\n",
      "24.424401707879305\n",
      "24.239005346819056\n",
      "24.115396924962802\n",
      "24.424191987566726\n",
      "23.924933080533783\n",
      "24.19484212027875\n",
      "24.117348378249833\n",
      "24.100690929662274\n",
      "23.76905109847816\n"
     ]
    }
   ],
   "source": [
    "for i in range(1, 20):\n",
    "    np.random.seed(1000)\n",
    "    x = np.random.random(i * 10) * (b - a) + a  \n",
    "    print(np.mean(f(x)) * (b - a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Symbolic Computation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Basics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "uuid": "f01d358d-8094-426c-8e69-657218d8c319"
   },
   "outputs": [],
   "source": [
    "import sympy as sy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "uuid": "2cb7d5d8-ae45-4001-863e-714df216a656"
   },
   "outputs": [],
   "source": [
    "x = sy.Symbol('x')  \n",
    "y = sy.Symbol('y')  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "uuid": "7bf55a76-f348-4820-af94-a83ed233d9a2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.core.symbol.Symbol"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "uuid": "a8f0388b-1df6-4389-877c-af5d9f141708"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sqrt(x)"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.sqrt(x)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "uuid": "f308fe2e-a5bc-4c88-a7f6-a4f09a568f2f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sqrt(x) - 13"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 + sy.sqrt(x) - 4 ** 2  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "uuid": "025f5084-4efc-4416-a564-b8a96ec426fd"
   },
   "outputs": [],
   "source": [
    "f = x ** 2 + 3 + 0.5 * x ** 2 + 3 / 2  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "uuid": "f427581e-50ba-45b9-a145-ff734be26e59"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5*x**2 + 4.5"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.simplify(f)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "uuid": "59837e7c-a82f-44e5-8b87-b0fba310ffc5"
   },
   "outputs": [],
   "source": [
    "sy.init_printing(pretty_print=False, use_unicode=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "uuid": "ea1bbb85-a431-4e6c-a264-6ffb6df9f59e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     2      \n",
      "1.5*x  + 4.5\n"
     ]
    }
   ],
   "source": [
    "print(sy.pretty(f))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "uuid": "e8702014-5347-4eac-b10c-39c5a54459c9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  ___      \n",
      "\\/ x  + 0.5\n"
     ]
    }
   ],
   "source": [
    "print(sy.pretty(sy.sqrt(x) + 0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 242 ms, sys: 6.17 ms, total: 248 ms\n",
      "Wall time: 248 ms\n"
     ]
    }
   ],
   "source": [
    "%time pi_str = str(sy.N(sy.pi, 400000))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "uuid": "b8cf7cf4-56e2-4c6b-a70b-6592ec4bd6a6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'3.1415926535897932384626433832795028841971'"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi_str[:42]  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "uuid": "595cc15e-99b8-43c7-ad89-db4500fdb860"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'8245672736856312185020980470362464176198'"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi_str[-40:]  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "uuid": "cc4b85c4-e603-4d36-9553-f3999e877fca"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 89 µs, sys: 0 ns, total: 89 µs\n",
      "Wall time: 94.2 µs\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "80847"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time pi_str.find('061072')  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "uuid": "c310eeab-ac04-4015-a327-29628f9a9a11"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-1, 1]"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solve(x ** 2 - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "uuid": "60076f9d-93f3-47e0-b5b6-87d1bca3d30a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-2, 2]"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solve(x ** 2 - 1 - 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "uuid": "6c9e1060-61e6-4b18-9be4-cb71b83fc5a7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.858094329496553, -0.679047164748276 - 0.839206763026694*I, -0.679047164748276 + 0.839206763026694*I]"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solve(x ** 3 + 0.5 * x ** 2 - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "uuid": "fcd70615-0db5-4c5c-8246-245ba3c8501c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{x: -I*y}, {x: I*y}]"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solve(x ** 2 + y ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Integration and Differentiation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "uuid": "503329d1-812a-461c-9019-e6bb2a44125e"
   },
   "outputs": [],
   "source": [
    "a, b = sy.symbols('a b')  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "I = sy.Integral(sy.sin(x) + 0.5 * x, (x, a, b))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "uuid": "af7bf980-d65b-4567-8576-404e79c5ac65"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  b                    \n",
      "  /                    \n",
      " |                     \n",
      " |  (0.5*x + sin(x)) dx\n",
      " |                     \n",
      "/                      \n",
      "a                      \n"
     ]
    }
   ],
   "source": [
    "print(sy.pretty(I))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "uuid": "89d4c980-01d7-423a-a2ab-a9698787019a"
   },
   "outputs": [],
   "source": [
    "int_func = sy.integrate(sy.sin(x) + 0.5 * x, x)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "uuid": "38141163-7d29-4bd6-bfaf-9f9cfad86967"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      2         \n",
      "0.25*x  - cos(x)\n"
     ]
    }
   ],
   "source": [
    "print(sy.pretty(int_func))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "uuid": "51d4481a-c6b6-4caa-b4d1-aa6fb04d4493"
   },
   "outputs": [],
   "source": [
    "Fb = int_func.subs(x, 9.5).evalf()  \n",
    "Fa = int_func.subs(x, 0.5).evalf()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "uuid": "0c46e097-c665-440e-9d05-03c0d6e6d8d8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.3747547180867"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Fb - Fa  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "int_func_limits = sy.integrate(sy.sin(x) + 0.5 * x, (x, a, b))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "uuid": "657b13dc-101e-4c0c-9d15-43dbd418c3c8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        2         2                  \n",
      "- 0.25*a  + 0.25*b  + cos(a) - cos(b)\n"
     ]
    }
   ],
   "source": [
    "print(sy.pretty(int_func_limits))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "uuid": "5c65cea8-1e15-4efa-aba4-52888becaf19"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.3747547180868"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_func_limits.subs({a : 0.5, b : 9.5}).evalf()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "uuid": "b13767c8-4878-42c1-b738-0727b824b329"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.3747547180867"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.integrate(sy.sin(x) + 0.5 * x, (x, 0.5, 9.5))  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Differentiation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "uuid": "6ea93bb3-eb7c-4837-8327-621f3752b657"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5*x + sin(x)"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_func.diff()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "uuid": "164131fd-a197-40ce-85d6-94221e808073"
   },
   "outputs": [],
   "source": [
    "f = (sy.sin(x) + 0.05 * x ** 2\n",
    "   + sy.sin(y) + 0.05 * y ** 2)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "uuid": "5d1ce51b-2536-469b-b516-56db1e86519a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1*x + cos(x)"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "del_x = sy.diff(f, x)  \n",
    "del_x  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "uuid": "8d778c21-ed6a-43f0-8347-b95af334972a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1*y + cos(y)"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "del_y = sy.diff(f, y)  \n",
    "del_y  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "uuid": "588daaba-266a-43da-a4b9-baeb56fc1ac8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.42755177876459"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xo = sy.nsolve(del_x, -1.5)  \n",
    "xo  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "uuid": "2ef9beca-58f2-470b-a50e-6292bffbf2e0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.42755177876459"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yo = sy.nsolve(del_y, -1.5)  \n",
    "yo  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "uuid": "c0812b29-c69f-4a30-aaf1-1447d1434cf4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.77572565314742"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs({x : xo, y : yo}).evalf()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "uuid": "fd89d904-eab3-4035-941a-785c6a3f36cb"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.74632928225285"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xo = sy.nsolve(del_x, 1.5)\n",
    "xo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "uuid": "cc99d8f4-e062-4c7e-85ae-46e96d3c8f19"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.74632928225285"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yo = sy.nsolve(del_y, 1.5)  \n",
    "yo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "uuid": "54622abe-cef1-47ff-bf23-b883cf588a91"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.27423381055640"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs({x : xo, y : yo}).evalf()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://tpq.io\" target=\"_blank\">http://tpq.io</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a> | <a href=\"mailto:training@tpq.io\">training@tpq.io</a>"
   ]
  }
 ],
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